#include "ed25519/fe.h"
#include "ed25519/fixedint.h"

/*
    helper functions
*/
static uint64_t
load_3(const unsigned char* in) {
  uint64_t result;

  result = (uint64_t)in[0];
  result |= ((uint64_t)in[1]) << 8;
  result |= ((uint64_t)in[2]) << 16;

  return result;
}

static uint64_t
load_4(const unsigned char* in) {
  uint64_t result;

  result = (uint64_t)in[0];
  result |= ((uint64_t)in[1]) << 8;
  result |= ((uint64_t)in[2]) << 16;
  result |= ((uint64_t)in[3]) << 24;

  return result;
}

/*
    h = 0
*/

void
fe_0(fe h) {
  h[0] = 0;
  h[1] = 0;
  h[2] = 0;
  h[3] = 0;
  h[4] = 0;
  h[5] = 0;
  h[6] = 0;
  h[7] = 0;
  h[8] = 0;
  h[9] = 0;
}

/*
    h = 1
*/

void
fe_1(fe h) {
  h[0] = 1;
  h[1] = 0;
  h[2] = 0;
  h[3] = 0;
  h[4] = 0;
  h[5] = 0;
  h[6] = 0;
  h[7] = 0;
  h[8] = 0;
  h[9] = 0;
}

/*
    h = f + g
    Can overlap h with f or g.

    Preconditions:
       |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
       |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

    Postconditions:
       |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/

void
fe_add(fe h, const fe f, const fe g) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t g0 = g[0];
  int32_t g1 = g[1];
  int32_t g2 = g[2];
  int32_t g3 = g[3];
  int32_t g4 = g[4];
  int32_t g5 = g[5];
  int32_t g6 = g[6];
  int32_t g7 = g[7];
  int32_t g8 = g[8];
  int32_t g9 = g[9];
  int32_t h0 = f0 + g0;
  int32_t h1 = f1 + g1;
  int32_t h2 = f2 + g2;
  int32_t h3 = f3 + g3;
  int32_t h4 = f4 + g4;
  int32_t h5 = f5 + g5;
  int32_t h6 = f6 + g6;
  int32_t h7 = f7 + g7;
  int32_t h8 = f8 + g8;
  int32_t h9 = f9 + g9;

  h[0] = h0;
  h[1] = h1;
  h[2] = h2;
  h[3] = h3;
  h[4] = h4;
  h[5] = h5;
  h[6] = h6;
  h[7] = h7;
  h[8] = h8;
  h[9] = h9;
}

/*
    Replace (f,g) with (g,g) if b == 1;
    replace (f,g) with (f,g) if b == 0.

    Preconditions: b in {0,1}.
*/

void
fe_cmov(fe f, const fe g, unsigned int b) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t g0 = g[0];
  int32_t g1 = g[1];
  int32_t g2 = g[2];
  int32_t g3 = g[3];
  int32_t g4 = g[4];
  int32_t g5 = g[5];
  int32_t g6 = g[6];
  int32_t g7 = g[7];
  int32_t g8 = g[8];
  int32_t g9 = g[9];
  int32_t x0 = f0 ^ g0;
  int32_t x1 = f1 ^ g1;
  int32_t x2 = f2 ^ g2;
  int32_t x3 = f3 ^ g3;
  int32_t x4 = f4 ^ g4;
  int32_t x5 = f5 ^ g5;
  int32_t x6 = f6 ^ g6;
  int32_t x7 = f7 ^ g7;
  int32_t x8 = f8 ^ g8;
  int32_t x9 = f9 ^ g9;

  b = (unsigned int)(-(int)b); /* silence warning */
  x0 &= b;
  x1 &= b;
  x2 &= b;
  x3 &= b;
  x4 &= b;
  x5 &= b;
  x6 &= b;
  x7 &= b;
  x8 &= b;
  x9 &= b;

  f[0] = f0 ^ x0;
  f[1] = f1 ^ x1;
  f[2] = f2 ^ x2;
  f[3] = f3 ^ x3;
  f[4] = f4 ^ x4;
  f[5] = f5 ^ x5;
  f[6] = f6 ^ x6;
  f[7] = f7 ^ x7;
  f[8] = f8 ^ x8;
  f[9] = f9 ^ x9;
}

/*
    Replace (f,g) with (g,f) if b == 1;
    replace (f,g) with (f,g) if b == 0.

    Preconditions: b in {0,1}.
*/

void
fe_cswap(fe f, fe g, unsigned int b) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t g0 = g[0];
  int32_t g1 = g[1];
  int32_t g2 = g[2];
  int32_t g3 = g[3];
  int32_t g4 = g[4];
  int32_t g5 = g[5];
  int32_t g6 = g[6];
  int32_t g7 = g[7];
  int32_t g8 = g[8];
  int32_t g9 = g[9];
  int32_t x0 = f0 ^ g0;
  int32_t x1 = f1 ^ g1;
  int32_t x2 = f2 ^ g2;
  int32_t x3 = f3 ^ g3;
  int32_t x4 = f4 ^ g4;
  int32_t x5 = f5 ^ g5;
  int32_t x6 = f6 ^ g6;
  int32_t x7 = f7 ^ g7;
  int32_t x8 = f8 ^ g8;
  int32_t x9 = f9 ^ g9;
  b          = (unsigned int)(-(int)b); /* silence warning */
  x0 &= b;
  x1 &= b;
  x2 &= b;
  x3 &= b;
  x4 &= b;
  x5 &= b;
  x6 &= b;
  x7 &= b;
  x8 &= b;
  x9 &= b;
  f[0] = f0 ^ x0;
  f[1] = f1 ^ x1;
  f[2] = f2 ^ x2;
  f[3] = f3 ^ x3;
  f[4] = f4 ^ x4;
  f[5] = f5 ^ x5;
  f[6] = f6 ^ x6;
  f[7] = f7 ^ x7;
  f[8] = f8 ^ x8;
  f[9] = f9 ^ x9;
  g[0] = g0 ^ x0;
  g[1] = g1 ^ x1;
  g[2] = g2 ^ x2;
  g[3] = g3 ^ x3;
  g[4] = g4 ^ x4;
  g[5] = g5 ^ x5;
  g[6] = g6 ^ x6;
  g[7] = g7 ^ x7;
  g[8] = g8 ^ x8;
  g[9] = g9 ^ x9;
}

/*
    h = f
*/

void
fe_copy(fe h, const fe f) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];

  h[0] = f0;
  h[1] = f1;
  h[2] = f2;
  h[3] = f3;
  h[4] = f4;
  h[5] = f5;
  h[6] = f6;
  h[7] = f7;
  h[8] = f8;
  h[9] = f9;
}

/*
    Ignores top bit of h.
*/

void
fe_frombytes(fe h, const unsigned char* s) {
  int64_t h0 = load_4(s);
  int64_t h1 = load_3(s + 4) << 6;
  int64_t h2 = load_3(s + 7) << 5;
  int64_t h3 = load_3(s + 10) << 3;
  int64_t h4 = load_3(s + 13) << 2;
  int64_t h5 = load_4(s + 16);
  int64_t h6 = load_3(s + 20) << 7;
  int64_t h7 = load_3(s + 23) << 5;
  int64_t h8 = load_3(s + 26) << 4;
  int64_t h9 = (load_3(s + 29) & 8388607) << 2;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;

  carry9 = (h9 + (int64_t)(1 << 24)) >> 25;
  h0 += carry9 * 19;
  h9 -= carry9 << 25;
  carry1 = (h1 + (int64_t)(1 << 24)) >> 25;
  h2 += carry1;
  h1 -= carry1 << 25;
  carry3 = (h3 + (int64_t)(1 << 24)) >> 25;
  h4 += carry3;
  h3 -= carry3 << 25;
  carry5 = (h5 + (int64_t)(1 << 24)) >> 25;
  h6 += carry5;
  h5 -= carry5 << 25;
  carry7 = (h7 + (int64_t)(1 << 24)) >> 25;
  h8 += carry7;
  h7 -= carry7 << 25;
  carry0 = (h0 + (int64_t)(1 << 25)) >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;
  carry2 = (h2 + (int64_t)(1 << 25)) >> 26;
  h3 += carry2;
  h2 -= carry2 << 26;
  carry4 = (h4 + (int64_t)(1 << 25)) >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;
  carry6 = (h6 + (int64_t)(1 << 25)) >> 26;
  h7 += carry6;
  h6 -= carry6 << 26;
  carry8 = (h8 + (int64_t)(1 << 25)) >> 26;
  h9 += carry8;
  h8 -= carry8 << 26;

  h[0] = (int32_t)h0;
  h[1] = (int32_t)h1;
  h[2] = (int32_t)h2;
  h[3] = (int32_t)h3;
  h[4] = (int32_t)h4;
  h[5] = (int32_t)h5;
  h[6] = (int32_t)h6;
  h[7] = (int32_t)h7;
  h[8] = (int32_t)h8;
  h[9] = (int32_t)h9;
}

void
fe_invert(fe out, const fe z) {
  fe t0;
  fe t1;
  fe t2;
  fe t3;
  int i;

  fe_sq(t0, z);

  for (i = 1; i < 1; ++i) {
    fe_sq(t0, t0);
  }

  fe_sq(t1, t0);

  for (i = 1; i < 2; ++i) {
    fe_sq(t1, t1);
  }

  fe_mul(t1, z, t1);
  fe_mul(t0, t0, t1);
  fe_sq(t2, t0);

  for (i = 1; i < 1; ++i) {
    fe_sq(t2, t2);
  }

  fe_mul(t1, t1, t2);
  fe_sq(t2, t1);

  for (i = 1; i < 5; ++i) {
    fe_sq(t2, t2);
  }

  fe_mul(t1, t2, t1);
  fe_sq(t2, t1);

  for (i = 1; i < 10; ++i) {
    fe_sq(t2, t2);
  }

  fe_mul(t2, t2, t1);
  fe_sq(t3, t2);

  for (i = 1; i < 20; ++i) {
    fe_sq(t3, t3);
  }

  fe_mul(t2, t3, t2);
  fe_sq(t2, t2);

  for (i = 1; i < 10; ++i) {
    fe_sq(t2, t2);
  }

  fe_mul(t1, t2, t1);
  fe_sq(t2, t1);

  for (i = 1; i < 50; ++i) {
    fe_sq(t2, t2);
  }

  fe_mul(t2, t2, t1);
  fe_sq(t3, t2);

  for (i = 1; i < 100; ++i) {
    fe_sq(t3, t3);
  }

  fe_mul(t2, t3, t2);
  fe_sq(t2, t2);

  for (i = 1; i < 50; ++i) {
    fe_sq(t2, t2);
  }

  fe_mul(t1, t2, t1);
  fe_sq(t1, t1);

  for (i = 1; i < 5; ++i) {
    fe_sq(t1, t1);
  }

  fe_mul(out, t1, t0);
}

/*
    return 1 if f is in {1,3,5,...,q-2}
    return 0 if f is in {0,2,4,...,q-1}

    Preconditions:
       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/

int
fe_isnegative(const fe f) {
  unsigned char s[32];

  fe_tobytes(s, f);

  return s[0] & 1;
}

/*
    return 1 if f == 0
    return 0 if f != 0

    Preconditions:
       |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/

int
fe_isnonzero(const fe f) {
  unsigned char s[32];
  unsigned char r;

  fe_tobytes(s, f);

  r = s[0];
#define F(i) r |= s[i]
  F(1);
  F(2);
  F(3);
  F(4);
  F(5);
  F(6);
  F(7);
  F(8);
  F(9);
  F(10);
  F(11);
  F(12);
  F(13);
  F(14);
  F(15);
  F(16);
  F(17);
  F(18);
  F(19);
  F(20);
  F(21);
  F(22);
  F(23);
  F(24);
  F(25);
  F(26);
  F(27);
  F(28);
  F(29);
  F(30);
  F(31);
#undef F

  return r != 0;
}

/*
    h = f * g
    Can overlap h with f or g.

    Preconditions:
       |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
       |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.

    Postconditions:
       |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
    */

/*
Notes on implementation strategy:

Using schoolbook multiplication.
Karatsuba would save a little in some cost models.

Most multiplications by 2 and 19 are 32-bit precomputations;
cheaper than 64-bit postcomputations.

There is one remaining multiplication by 19 in the carry chain;
one *19 precomputation can be merged into this,
but the resulting data flow is considerably less clean.

There are 12 carries below.
10 of them are 2-way parallelizable and vectorizable.
Can get away with 11 carries, but then data flow is much deeper.

With tighter constraints on inputs can squeeze carries into int32.
*/

void
fe_mul(fe h, const fe f, const fe g) {
  int32_t f0      = f[0];
  int32_t f1      = f[1];
  int32_t f2      = f[2];
  int32_t f3      = f[3];
  int32_t f4      = f[4];
  int32_t f5      = f[5];
  int32_t f6      = f[6];
  int32_t f7      = f[7];
  int32_t f8      = f[8];
  int32_t f9      = f[9];
  int32_t g0      = g[0];
  int32_t g1      = g[1];
  int32_t g2      = g[2];
  int32_t g3      = g[3];
  int32_t g4      = g[4];
  int32_t g5      = g[5];
  int32_t g6      = g[6];
  int32_t g7      = g[7];
  int32_t g8      = g[8];
  int32_t g9      = g[9];
  int32_t g1_19   = 19 * g1; /* 1.959375*2^29 */
  int32_t g2_19   = 19 * g2; /* 1.959375*2^30; still ok */
  int32_t g3_19   = 19 * g3;
  int32_t g4_19   = 19 * g4;
  int32_t g5_19   = 19 * g5;
  int32_t g6_19   = 19 * g6;
  int32_t g7_19   = 19 * g7;
  int32_t g8_19   = 19 * g8;
  int32_t g9_19   = 19 * g9;
  int32_t f1_2    = 2 * f1;
  int32_t f3_2    = 2 * f3;
  int32_t f5_2    = 2 * f5;
  int32_t f7_2    = 2 * f7;
  int32_t f9_2    = 2 * f9;
  int64_t f0g0    = f0 * (int64_t)g0;
  int64_t f0g1    = f0 * (int64_t)g1;
  int64_t f0g2    = f0 * (int64_t)g2;
  int64_t f0g3    = f0 * (int64_t)g3;
  int64_t f0g4    = f0 * (int64_t)g4;
  int64_t f0g5    = f0 * (int64_t)g5;
  int64_t f0g6    = f0 * (int64_t)g6;
  int64_t f0g7    = f0 * (int64_t)g7;
  int64_t f0g8    = f0 * (int64_t)g8;
  int64_t f0g9    = f0 * (int64_t)g9;
  int64_t f1g0    = f1 * (int64_t)g0;
  int64_t f1g1_2  = f1_2 * (int64_t)g1;
  int64_t f1g2    = f1 * (int64_t)g2;
  int64_t f1g3_2  = f1_2 * (int64_t)g3;
  int64_t f1g4    = f1 * (int64_t)g4;
  int64_t f1g5_2  = f1_2 * (int64_t)g5;
  int64_t f1g6    = f1 * (int64_t)g6;
  int64_t f1g7_2  = f1_2 * (int64_t)g7;
  int64_t f1g8    = f1 * (int64_t)g8;
  int64_t f1g9_38 = f1_2 * (int64_t)g9_19;
  int64_t f2g0    = f2 * (int64_t)g0;
  int64_t f2g1    = f2 * (int64_t)g1;
  int64_t f2g2    = f2 * (int64_t)g2;
  int64_t f2g3    = f2 * (int64_t)g3;
  int64_t f2g4    = f2 * (int64_t)g4;
  int64_t f2g5    = f2 * (int64_t)g5;
  int64_t f2g6    = f2 * (int64_t)g6;
  int64_t f2g7    = f2 * (int64_t)g7;
  int64_t f2g8_19 = f2 * (int64_t)g8_19;
  int64_t f2g9_19 = f2 * (int64_t)g9_19;
  int64_t f3g0    = f3 * (int64_t)g0;
  int64_t f3g1_2  = f3_2 * (int64_t)g1;
  int64_t f3g2    = f3 * (int64_t)g2;
  int64_t f3g3_2  = f3_2 * (int64_t)g3;
  int64_t f3g4    = f3 * (int64_t)g4;
  int64_t f3g5_2  = f3_2 * (int64_t)g5;
  int64_t f3g6    = f3 * (int64_t)g6;
  int64_t f3g7_38 = f3_2 * (int64_t)g7_19;
  int64_t f3g8_19 = f3 * (int64_t)g8_19;
  int64_t f3g9_38 = f3_2 * (int64_t)g9_19;
  int64_t f4g0    = f4 * (int64_t)g0;
  int64_t f4g1    = f4 * (int64_t)g1;
  int64_t f4g2    = f4 * (int64_t)g2;
  int64_t f4g3    = f4 * (int64_t)g3;
  int64_t f4g4    = f4 * (int64_t)g4;
  int64_t f4g5    = f4 * (int64_t)g5;
  int64_t f4g6_19 = f4 * (int64_t)g6_19;
  int64_t f4g7_19 = f4 * (int64_t)g7_19;
  int64_t f4g8_19 = f4 * (int64_t)g8_19;
  int64_t f4g9_19 = f4 * (int64_t)g9_19;
  int64_t f5g0    = f5 * (int64_t)g0;
  int64_t f5g1_2  = f5_2 * (int64_t)g1;
  int64_t f5g2    = f5 * (int64_t)g2;
  int64_t f5g3_2  = f5_2 * (int64_t)g3;
  int64_t f5g4    = f5 * (int64_t)g4;
  int64_t f5g5_38 = f5_2 * (int64_t)g5_19;
  int64_t f5g6_19 = f5 * (int64_t)g6_19;
  int64_t f5g7_38 = f5_2 * (int64_t)g7_19;
  int64_t f5g8_19 = f5 * (int64_t)g8_19;
  int64_t f5g9_38 = f5_2 * (int64_t)g9_19;
  int64_t f6g0    = f6 * (int64_t)g0;
  int64_t f6g1    = f6 * (int64_t)g1;
  int64_t f6g2    = f6 * (int64_t)g2;
  int64_t f6g3    = f6 * (int64_t)g3;
  int64_t f6g4_19 = f6 * (int64_t)g4_19;
  int64_t f6g5_19 = f6 * (int64_t)g5_19;
  int64_t f6g6_19 = f6 * (int64_t)g6_19;
  int64_t f6g7_19 = f6 * (int64_t)g7_19;
  int64_t f6g8_19 = f6 * (int64_t)g8_19;
  int64_t f6g9_19 = f6 * (int64_t)g9_19;
  int64_t f7g0    = f7 * (int64_t)g0;
  int64_t f7g1_2  = f7_2 * (int64_t)g1;
  int64_t f7g2    = f7 * (int64_t)g2;
  int64_t f7g3_38 = f7_2 * (int64_t)g3_19;
  int64_t f7g4_19 = f7 * (int64_t)g4_19;
  int64_t f7g5_38 = f7_2 * (int64_t)g5_19;
  int64_t f7g6_19 = f7 * (int64_t)g6_19;
  int64_t f7g7_38 = f7_2 * (int64_t)g7_19;
  int64_t f7g8_19 = f7 * (int64_t)g8_19;
  int64_t f7g9_38 = f7_2 * (int64_t)g9_19;
  int64_t f8g0    = f8 * (int64_t)g0;
  int64_t f8g1    = f8 * (int64_t)g1;
  int64_t f8g2_19 = f8 * (int64_t)g2_19;
  int64_t f8g3_19 = f8 * (int64_t)g3_19;
  int64_t f8g4_19 = f8 * (int64_t)g4_19;
  int64_t f8g5_19 = f8 * (int64_t)g5_19;
  int64_t f8g6_19 = f8 * (int64_t)g6_19;
  int64_t f8g7_19 = f8 * (int64_t)g7_19;
  int64_t f8g8_19 = f8 * (int64_t)g8_19;
  int64_t f8g9_19 = f8 * (int64_t)g9_19;
  int64_t f9g0    = f9 * (int64_t)g0;
  int64_t f9g1_38 = f9_2 * (int64_t)g1_19;
  int64_t f9g2_19 = f9 * (int64_t)g2_19;
  int64_t f9g3_38 = f9_2 * (int64_t)g3_19;
  int64_t f9g4_19 = f9 * (int64_t)g4_19;
  int64_t f9g5_38 = f9_2 * (int64_t)g5_19;
  int64_t f9g6_19 = f9 * (int64_t)g6_19;
  int64_t f9g7_38 = f9_2 * (int64_t)g7_19;
  int64_t f9g8_19 = f9 * (int64_t)g8_19;
  int64_t f9g9_38 = f9_2 * (int64_t)g9_19;
  int64_t h0      = f0g0 + f1g9_38 + f2g8_19 + f3g7_38 + f4g6_19 + f5g5_38 +
               f6g4_19 + f7g3_38 + f8g2_19 + f9g1_38;
  int64_t h1 = f0g1 + f1g0 + f2g9_19 + f3g8_19 + f4g7_19 + f5g6_19 + f6g5_19 +
               f7g4_19 + f8g3_19 + f9g2_19;
  int64_t h2 = f0g2 + f1g1_2 + f2g0 + f3g9_38 + f4g8_19 + f5g7_38 + f6g6_19 +
               f7g5_38 + f8g4_19 + f9g3_38;
  int64_t h3 = f0g3 + f1g2 + f2g1 + f3g0 + f4g9_19 + f5g8_19 + f6g7_19 +
               f7g6_19 + f8g5_19 + f9g4_19;
  int64_t h4 = f0g4 + f1g3_2 + f2g2 + f3g1_2 + f4g0 + f5g9_38 + f6g8_19 +
               f7g7_38 + f8g6_19 + f9g5_38;
  int64_t h5 = f0g5 + f1g4 + f2g3 + f3g2 + f4g1 + f5g0 + f6g9_19 + f7g8_19 +
               f8g7_19 + f9g6_19;
  int64_t h6 = f0g6 + f1g5_2 + f2g4 + f3g3_2 + f4g2 + f5g1_2 + f6g0 + f7g9_38 +
               f8g8_19 + f9g7_38;
  int64_t h7 =
      f0g7 + f1g6 + f2g5 + f3g4 + f4g3 + f5g2 + f6g1 + f7g0 + f8g9_19 + f9g8_19;
  int64_t h8 = f0g8 + f1g7_2 + f2g6 + f3g5_2 + f4g4 + f5g3_2 + f6g2 + f7g1_2 +
               f8g0 + f9g9_38;
  int64_t h9 =
      f0g9 + f1g8 + f2g7 + f3g6 + f4g5 + f5g4 + f6g3 + f7g2 + f8g1 + f9g0;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;

  carry0 = (h0 + (int64_t)(1 << 25)) >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;
  carry4 = (h4 + (int64_t)(1 << 25)) >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;

  carry1 = (h1 + (int64_t)(1 << 24)) >> 25;
  h2 += carry1;
  h1 -= carry1 << 25;
  carry5 = (h5 + (int64_t)(1 << 24)) >> 25;
  h6 += carry5;
  h5 -= carry5 << 25;

  carry2 = (h2 + (int64_t)(1 << 25)) >> 26;
  h3 += carry2;
  h2 -= carry2 << 26;
  carry6 = (h6 + (int64_t)(1 << 25)) >> 26;
  h7 += carry6;
  h6 -= carry6 << 26;

  carry3 = (h3 + (int64_t)(1 << 24)) >> 25;
  h4 += carry3;
  h3 -= carry3 << 25;
  carry7 = (h7 + (int64_t)(1 << 24)) >> 25;
  h8 += carry7;
  h7 -= carry7 << 25;

  carry4 = (h4 + (int64_t)(1 << 25)) >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;
  carry8 = (h8 + (int64_t)(1 << 25)) >> 26;
  h9 += carry8;
  h8 -= carry8 << 26;

  carry9 = (h9 + (int64_t)(1 << 24)) >> 25;
  h0 += carry9 * 19;
  h9 -= carry9 << 25;

  carry0 = (h0 + (int64_t)(1 << 25)) >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;

  h[0] = (int32_t)h0;
  h[1] = (int32_t)h1;
  h[2] = (int32_t)h2;
  h[3] = (int32_t)h3;
  h[4] = (int32_t)h4;
  h[5] = (int32_t)h5;
  h[6] = (int32_t)h6;
  h[7] = (int32_t)h7;
  h[8] = (int32_t)h8;
  h[9] = (int32_t)h9;
}

/*
h = f * 121666
Can overlap h with f.

Preconditions:
   |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Postconditions:
   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/

void
fe_mul121666(fe h, fe f) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int64_t h0 = f0 * (int64_t)121666;
  int64_t h1 = f1 * (int64_t)121666;
  int64_t h2 = f2 * (int64_t)121666;
  int64_t h3 = f3 * (int64_t)121666;
  int64_t h4 = f4 * (int64_t)121666;
  int64_t h5 = f5 * (int64_t)121666;
  int64_t h6 = f6 * (int64_t)121666;
  int64_t h7 = f7 * (int64_t)121666;
  int64_t h8 = f8 * (int64_t)121666;
  int64_t h9 = f9 * (int64_t)121666;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;

  carry9 = (h9 + (int64_t)(1 << 24)) >> 25;
  h0 += carry9 * 19;
  h9 -= carry9 << 25;
  carry1 = (h1 + (int64_t)(1 << 24)) >> 25;
  h2 += carry1;
  h1 -= carry1 << 25;
  carry3 = (h3 + (int64_t)(1 << 24)) >> 25;
  h4 += carry3;
  h3 -= carry3 << 25;
  carry5 = (h5 + (int64_t)(1 << 24)) >> 25;
  h6 += carry5;
  h5 -= carry5 << 25;
  carry7 = (h7 + (int64_t)(1 << 24)) >> 25;
  h8 += carry7;
  h7 -= carry7 << 25;

  carry0 = (h0 + (int64_t)(1 << 25)) >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;
  carry2 = (h2 + (int64_t)(1 << 25)) >> 26;
  h3 += carry2;
  h2 -= carry2 << 26;
  carry4 = (h4 + (int64_t)(1 << 25)) >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;
  carry6 = (h6 + (int64_t)(1 << 25)) >> 26;
  h7 += carry6;
  h6 -= carry6 << 26;
  carry8 = (h8 + (int64_t)(1 << 25)) >> 26;
  h9 += carry8;
  h8 -= carry8 << 26;

  h[0] = (int32_t)h0;
  h[1] = (int32_t)h1;
  h[2] = (int32_t)h2;
  h[3] = (int32_t)h3;
  h[4] = (int32_t)h4;
  h[5] = (int32_t)h5;
  h[6] = (int32_t)h6;
  h[7] = (int32_t)h7;
  h[8] = (int32_t)h8;
  h[9] = (int32_t)h9;
}

/*
h = -f

Preconditions:
   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

Postconditions:
   |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
*/

void
fe_neg(fe h, const fe f) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t h0 = -f0;
  int32_t h1 = -f1;
  int32_t h2 = -f2;
  int32_t h3 = -f3;
  int32_t h4 = -f4;
  int32_t h5 = -f5;
  int32_t h6 = -f6;
  int32_t h7 = -f7;
  int32_t h8 = -f8;
  int32_t h9 = -f9;

  h[0] = h0;
  h[1] = h1;
  h[2] = h2;
  h[3] = h3;
  h[4] = h4;
  h[5] = h5;
  h[6] = h6;
  h[7] = h7;
  h[8] = h8;
  h[9] = h9;
}

void
fe_pow22523(fe out, const fe z) {
  fe t0;
  fe t1;
  fe t2;
  int i;
  fe_sq(t0, z);

  for (i = 1; i < 1; ++i) {
    fe_sq(t0, t0);
  }

  fe_sq(t1, t0);

  for (i = 1; i < 2; ++i) {
    fe_sq(t1, t1);
  }

  fe_mul(t1, z, t1);
  fe_mul(t0, t0, t1);
  fe_sq(t0, t0);

  for (i = 1; i < 1; ++i) {
    fe_sq(t0, t0);
  }

  fe_mul(t0, t1, t0);
  fe_sq(t1, t0);

  for (i = 1; i < 5; ++i) {
    fe_sq(t1, t1);
  }

  fe_mul(t0, t1, t0);
  fe_sq(t1, t0);

  for (i = 1; i < 10; ++i) {
    fe_sq(t1, t1);
  }

  fe_mul(t1, t1, t0);
  fe_sq(t2, t1);

  for (i = 1; i < 20; ++i) {
    fe_sq(t2, t2);
  }

  fe_mul(t1, t2, t1);
  fe_sq(t1, t1);

  for (i = 1; i < 10; ++i) {
    fe_sq(t1, t1);
  }

  fe_mul(t0, t1, t0);
  fe_sq(t1, t0);

  for (i = 1; i < 50; ++i) {
    fe_sq(t1, t1);
  }

  fe_mul(t1, t1, t0);
  fe_sq(t2, t1);

  for (i = 1; i < 100; ++i) {
    fe_sq(t2, t2);
  }

  fe_mul(t1, t2, t1);
  fe_sq(t1, t1);

  for (i = 1; i < 50; ++i) {
    fe_sq(t1, t1);
  }

  fe_mul(t0, t1, t0);
  fe_sq(t0, t0);

  for (i = 1; i < 2; ++i) {
    fe_sq(t0, t0);
  }

  fe_mul(out, t0, z);
  return;
}

/*
h = f * f
Can overlap h with f.

Preconditions:
   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.

Postconditions:
   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/

/*
See fe_mul.c for discussion of implementation strategy.
*/

void
fe_sq(fe h, const fe f) {
  int32_t f0      = f[0];
  int32_t f1      = f[1];
  int32_t f2      = f[2];
  int32_t f3      = f[3];
  int32_t f4      = f[4];
  int32_t f5      = f[5];
  int32_t f6      = f[6];
  int32_t f7      = f[7];
  int32_t f8      = f[8];
  int32_t f9      = f[9];
  int32_t f0_2    = 2 * f0;
  int32_t f1_2    = 2 * f1;
  int32_t f2_2    = 2 * f2;
  int32_t f3_2    = 2 * f3;
  int32_t f4_2    = 2 * f4;
  int32_t f5_2    = 2 * f5;
  int32_t f6_2    = 2 * f6;
  int32_t f7_2    = 2 * f7;
  int32_t f5_38   = 38 * f5; /* 1.959375*2^30 */
  int32_t f6_19   = 19 * f6; /* 1.959375*2^30 */
  int32_t f7_38   = 38 * f7; /* 1.959375*2^30 */
  int32_t f8_19   = 19 * f8; /* 1.959375*2^30 */
  int32_t f9_38   = 38 * f9; /* 1.959375*2^30 */
  int64_t f0f0    = f0 * (int64_t)f0;
  int64_t f0f1_2  = f0_2 * (int64_t)f1;
  int64_t f0f2_2  = f0_2 * (int64_t)f2;
  int64_t f0f3_2  = f0_2 * (int64_t)f3;
  int64_t f0f4_2  = f0_2 * (int64_t)f4;
  int64_t f0f5_2  = f0_2 * (int64_t)f5;
  int64_t f0f6_2  = f0_2 * (int64_t)f6;
  int64_t f0f7_2  = f0_2 * (int64_t)f7;
  int64_t f0f8_2  = f0_2 * (int64_t)f8;
  int64_t f0f9_2  = f0_2 * (int64_t)f9;
  int64_t f1f1_2  = f1_2 * (int64_t)f1;
  int64_t f1f2_2  = f1_2 * (int64_t)f2;
  int64_t f1f3_4  = f1_2 * (int64_t)f3_2;
  int64_t f1f4_2  = f1_2 * (int64_t)f4;
  int64_t f1f5_4  = f1_2 * (int64_t)f5_2;
  int64_t f1f6_2  = f1_2 * (int64_t)f6;
  int64_t f1f7_4  = f1_2 * (int64_t)f7_2;
  int64_t f1f8_2  = f1_2 * (int64_t)f8;
  int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
  int64_t f2f2    = f2 * (int64_t)f2;
  int64_t f2f3_2  = f2_2 * (int64_t)f3;
  int64_t f2f4_2  = f2_2 * (int64_t)f4;
  int64_t f2f5_2  = f2_2 * (int64_t)f5;
  int64_t f2f6_2  = f2_2 * (int64_t)f6;
  int64_t f2f7_2  = f2_2 * (int64_t)f7;
  int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
  int64_t f2f9_38 = f2 * (int64_t)f9_38;
  int64_t f3f3_2  = f3_2 * (int64_t)f3;
  int64_t f3f4_2  = f3_2 * (int64_t)f4;
  int64_t f3f5_4  = f3_2 * (int64_t)f5_2;
  int64_t f3f6_2  = f3_2 * (int64_t)f6;
  int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
  int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
  int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
  int64_t f4f4    = f4 * (int64_t)f4;
  int64_t f4f5_2  = f4_2 * (int64_t)f5;
  int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
  int64_t f4f7_38 = f4 * (int64_t)f7_38;
  int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
  int64_t f4f9_38 = f4 * (int64_t)f9_38;
  int64_t f5f5_38 = f5 * (int64_t)f5_38;
  int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
  int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
  int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
  int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
  int64_t f6f6_19 = f6 * (int64_t)f6_19;
  int64_t f6f7_38 = f6 * (int64_t)f7_38;
  int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
  int64_t f6f9_38 = f6 * (int64_t)f9_38;
  int64_t f7f7_38 = f7 * (int64_t)f7_38;
  int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
  int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
  int64_t f8f8_19 = f8 * (int64_t)f8_19;
  int64_t f8f9_38 = f8 * (int64_t)f9_38;
  int64_t f9f9_38 = f9 * (int64_t)f9_38;
  int64_t h0      = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
  int64_t h1      = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
  int64_t h2      = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
  int64_t h3      = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
  int64_t h4      = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
  int64_t h5      = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
  int64_t h6      = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
  int64_t h7      = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
  int64_t h8      = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
  int64_t h9      = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;
  carry0 = (h0 + (int64_t)(1 << 25)) >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;
  carry4 = (h4 + (int64_t)(1 << 25)) >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;
  carry1 = (h1 + (int64_t)(1 << 24)) >> 25;
  h2 += carry1;
  h1 -= carry1 << 25;
  carry5 = (h5 + (int64_t)(1 << 24)) >> 25;
  h6 += carry5;
  h5 -= carry5 << 25;
  carry2 = (h2 + (int64_t)(1 << 25)) >> 26;
  h3 += carry2;
  h2 -= carry2 << 26;
  carry6 = (h6 + (int64_t)(1 << 25)) >> 26;
  h7 += carry6;
  h6 -= carry6 << 26;
  carry3 = (h3 + (int64_t)(1 << 24)) >> 25;
  h4 += carry3;
  h3 -= carry3 << 25;
  carry7 = (h7 + (int64_t)(1 << 24)) >> 25;
  h8 += carry7;
  h7 -= carry7 << 25;
  carry4 = (h4 + (int64_t)(1 << 25)) >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;
  carry8 = (h8 + (int64_t)(1 << 25)) >> 26;
  h9 += carry8;
  h8 -= carry8 << 26;
  carry9 = (h9 + (int64_t)(1 << 24)) >> 25;
  h0 += carry9 * 19;
  h9 -= carry9 << 25;
  carry0 = (h0 + (int64_t)(1 << 25)) >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;
  h[0] = (int32_t)h0;
  h[1] = (int32_t)h1;
  h[2] = (int32_t)h2;
  h[3] = (int32_t)h3;
  h[4] = (int32_t)h4;
  h[5] = (int32_t)h5;
  h[6] = (int32_t)h6;
  h[7] = (int32_t)h7;
  h[8] = (int32_t)h8;
  h[9] = (int32_t)h9;
}

/*
h = 2 * f * f
Can overlap h with f.

Preconditions:
   |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.

Postconditions:
   |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
*/

/*
See fe_mul.c for discussion of implementation strategy.
*/

void
fe_sq2(fe h, const fe f) {
  int32_t f0      = f[0];
  int32_t f1      = f[1];
  int32_t f2      = f[2];
  int32_t f3      = f[3];
  int32_t f4      = f[4];
  int32_t f5      = f[5];
  int32_t f6      = f[6];
  int32_t f7      = f[7];
  int32_t f8      = f[8];
  int32_t f9      = f[9];
  int32_t f0_2    = 2 * f0;
  int32_t f1_2    = 2 * f1;
  int32_t f2_2    = 2 * f2;
  int32_t f3_2    = 2 * f3;
  int32_t f4_2    = 2 * f4;
  int32_t f5_2    = 2 * f5;
  int32_t f6_2    = 2 * f6;
  int32_t f7_2    = 2 * f7;
  int32_t f5_38   = 38 * f5; /* 1.959375*2^30 */
  int32_t f6_19   = 19 * f6; /* 1.959375*2^30 */
  int32_t f7_38   = 38 * f7; /* 1.959375*2^30 */
  int32_t f8_19   = 19 * f8; /* 1.959375*2^30 */
  int32_t f9_38   = 38 * f9; /* 1.959375*2^30 */
  int64_t f0f0    = f0 * (int64_t)f0;
  int64_t f0f1_2  = f0_2 * (int64_t)f1;
  int64_t f0f2_2  = f0_2 * (int64_t)f2;
  int64_t f0f3_2  = f0_2 * (int64_t)f3;
  int64_t f0f4_2  = f0_2 * (int64_t)f4;
  int64_t f0f5_2  = f0_2 * (int64_t)f5;
  int64_t f0f6_2  = f0_2 * (int64_t)f6;
  int64_t f0f7_2  = f0_2 * (int64_t)f7;
  int64_t f0f8_2  = f0_2 * (int64_t)f8;
  int64_t f0f9_2  = f0_2 * (int64_t)f9;
  int64_t f1f1_2  = f1_2 * (int64_t)f1;
  int64_t f1f2_2  = f1_2 * (int64_t)f2;
  int64_t f1f3_4  = f1_2 * (int64_t)f3_2;
  int64_t f1f4_2  = f1_2 * (int64_t)f4;
  int64_t f1f5_4  = f1_2 * (int64_t)f5_2;
  int64_t f1f6_2  = f1_2 * (int64_t)f6;
  int64_t f1f7_4  = f1_2 * (int64_t)f7_2;
  int64_t f1f8_2  = f1_2 * (int64_t)f8;
  int64_t f1f9_76 = f1_2 * (int64_t)f9_38;
  int64_t f2f2    = f2 * (int64_t)f2;
  int64_t f2f3_2  = f2_2 * (int64_t)f3;
  int64_t f2f4_2  = f2_2 * (int64_t)f4;
  int64_t f2f5_2  = f2_2 * (int64_t)f5;
  int64_t f2f6_2  = f2_2 * (int64_t)f6;
  int64_t f2f7_2  = f2_2 * (int64_t)f7;
  int64_t f2f8_38 = f2_2 * (int64_t)f8_19;
  int64_t f2f9_38 = f2 * (int64_t)f9_38;
  int64_t f3f3_2  = f3_2 * (int64_t)f3;
  int64_t f3f4_2  = f3_2 * (int64_t)f4;
  int64_t f3f5_4  = f3_2 * (int64_t)f5_2;
  int64_t f3f6_2  = f3_2 * (int64_t)f6;
  int64_t f3f7_76 = f3_2 * (int64_t)f7_38;
  int64_t f3f8_38 = f3_2 * (int64_t)f8_19;
  int64_t f3f9_76 = f3_2 * (int64_t)f9_38;
  int64_t f4f4    = f4 * (int64_t)f4;
  int64_t f4f5_2  = f4_2 * (int64_t)f5;
  int64_t f4f6_38 = f4_2 * (int64_t)f6_19;
  int64_t f4f7_38 = f4 * (int64_t)f7_38;
  int64_t f4f8_38 = f4_2 * (int64_t)f8_19;
  int64_t f4f9_38 = f4 * (int64_t)f9_38;
  int64_t f5f5_38 = f5 * (int64_t)f5_38;
  int64_t f5f6_38 = f5_2 * (int64_t)f6_19;
  int64_t f5f7_76 = f5_2 * (int64_t)f7_38;
  int64_t f5f8_38 = f5_2 * (int64_t)f8_19;
  int64_t f5f9_76 = f5_2 * (int64_t)f9_38;
  int64_t f6f6_19 = f6 * (int64_t)f6_19;
  int64_t f6f7_38 = f6 * (int64_t)f7_38;
  int64_t f6f8_38 = f6_2 * (int64_t)f8_19;
  int64_t f6f9_38 = f6 * (int64_t)f9_38;
  int64_t f7f7_38 = f7 * (int64_t)f7_38;
  int64_t f7f8_38 = f7_2 * (int64_t)f8_19;
  int64_t f7f9_76 = f7_2 * (int64_t)f9_38;
  int64_t f8f8_19 = f8 * (int64_t)f8_19;
  int64_t f8f9_38 = f8 * (int64_t)f9_38;
  int64_t f9f9_38 = f9 * (int64_t)f9_38;
  int64_t h0      = f0f0 + f1f9_76 + f2f8_38 + f3f7_76 + f4f6_38 + f5f5_38;
  int64_t h1      = f0f1_2 + f2f9_38 + f3f8_38 + f4f7_38 + f5f6_38;
  int64_t h2      = f0f2_2 + f1f1_2 + f3f9_76 + f4f8_38 + f5f7_76 + f6f6_19;
  int64_t h3      = f0f3_2 + f1f2_2 + f4f9_38 + f5f8_38 + f6f7_38;
  int64_t h4      = f0f4_2 + f1f3_4 + f2f2 + f5f9_76 + f6f8_38 + f7f7_38;
  int64_t h5      = f0f5_2 + f1f4_2 + f2f3_2 + f6f9_38 + f7f8_38;
  int64_t h6      = f0f6_2 + f1f5_4 + f2f4_2 + f3f3_2 + f7f9_76 + f8f8_19;
  int64_t h7      = f0f7_2 + f1f6_2 + f2f5_2 + f3f4_2 + f8f9_38;
  int64_t h8      = f0f8_2 + f1f7_4 + f2f6_2 + f3f5_4 + f4f4 + f9f9_38;
  int64_t h9      = f0f9_2 + f1f8_2 + f2f7_2 + f3f6_2 + f4f5_2;
  int64_t carry0;
  int64_t carry1;
  int64_t carry2;
  int64_t carry3;
  int64_t carry4;
  int64_t carry5;
  int64_t carry6;
  int64_t carry7;
  int64_t carry8;
  int64_t carry9;
  h0 += h0;
  h1 += h1;
  h2 += h2;
  h3 += h3;
  h4 += h4;
  h5 += h5;
  h6 += h6;
  h7 += h7;
  h8 += h8;
  h9 += h9;
  carry0 = (h0 + (int64_t)(1 << 25)) >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;
  carry4 = (h4 + (int64_t)(1 << 25)) >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;
  carry1 = (h1 + (int64_t)(1 << 24)) >> 25;
  h2 += carry1;
  h1 -= carry1 << 25;
  carry5 = (h5 + (int64_t)(1 << 24)) >> 25;
  h6 += carry5;
  h5 -= carry5 << 25;
  carry2 = (h2 + (int64_t)(1 << 25)) >> 26;
  h3 += carry2;
  h2 -= carry2 << 26;
  carry6 = (h6 + (int64_t)(1 << 25)) >> 26;
  h7 += carry6;
  h6 -= carry6 << 26;
  carry3 = (h3 + (int64_t)(1 << 24)) >> 25;
  h4 += carry3;
  h3 -= carry3 << 25;
  carry7 = (h7 + (int64_t)(1 << 24)) >> 25;
  h8 += carry7;
  h7 -= carry7 << 25;
  carry4 = (h4 + (int64_t)(1 << 25)) >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;
  carry8 = (h8 + (int64_t)(1 << 25)) >> 26;
  h9 += carry8;
  h8 -= carry8 << 26;
  carry9 = (h9 + (int64_t)(1 << 24)) >> 25;
  h0 += carry9 * 19;
  h9 -= carry9 << 25;
  carry0 = (h0 + (int64_t)(1 << 25)) >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;
  h[0] = (int32_t)h0;
  h[1] = (int32_t)h1;
  h[2] = (int32_t)h2;
  h[3] = (int32_t)h3;
  h[4] = (int32_t)h4;
  h[5] = (int32_t)h5;
  h[6] = (int32_t)h6;
  h[7] = (int32_t)h7;
  h[8] = (int32_t)h8;
  h[9] = (int32_t)h9;
}

/*
h = f - g
Can overlap h with f or g.

Preconditions:
   |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
   |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.

Postconditions:
   |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
*/

void
fe_sub(fe h, const fe f, const fe g) {
  int32_t f0 = f[0];
  int32_t f1 = f[1];
  int32_t f2 = f[2];
  int32_t f3 = f[3];
  int32_t f4 = f[4];
  int32_t f5 = f[5];
  int32_t f6 = f[6];
  int32_t f7 = f[7];
  int32_t f8 = f[8];
  int32_t f9 = f[9];
  int32_t g0 = g[0];
  int32_t g1 = g[1];
  int32_t g2 = g[2];
  int32_t g3 = g[3];
  int32_t g4 = g[4];
  int32_t g5 = g[5];
  int32_t g6 = g[6];
  int32_t g7 = g[7];
  int32_t g8 = g[8];
  int32_t g9 = g[9];
  int32_t h0 = f0 - g0;
  int32_t h1 = f1 - g1;
  int32_t h2 = f2 - g2;
  int32_t h3 = f3 - g3;
  int32_t h4 = f4 - g4;
  int32_t h5 = f5 - g5;
  int32_t h6 = f6 - g6;
  int32_t h7 = f7 - g7;
  int32_t h8 = f8 - g8;
  int32_t h9 = f9 - g9;

  h[0] = h0;
  h[1] = h1;
  h[2] = h2;
  h[3] = h3;
  h[4] = h4;
  h[5] = h5;
  h[6] = h6;
  h[7] = h7;
  h[8] = h8;
  h[9] = h9;
}

/*
Preconditions:
  |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.

Write p=2^255-19; q=floor(h/p).
Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).

Proof:
  Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
  Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.

  Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
  Then 0<y<1.

  Write r=h-pq.
  Have 0<=r<=p-1=2^255-20.
  Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1.

  Write x=r+19(2^-255)r+y.
  Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q.

  Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1))
  so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q.
*/

void
fe_tobytes(unsigned char* s, const fe h) {
  int32_t h0 = h[0];
  int32_t h1 = h[1];
  int32_t h2 = h[2];
  int32_t h3 = h[3];
  int32_t h4 = h[4];
  int32_t h5 = h[5];
  int32_t h6 = h[6];
  int32_t h7 = h[7];
  int32_t h8 = h[8];
  int32_t h9 = h[9];
  int32_t q;
  int32_t carry0;
  int32_t carry1;
  int32_t carry2;
  int32_t carry3;
  int32_t carry4;
  int32_t carry5;
  int32_t carry6;
  int32_t carry7;
  int32_t carry8;
  int32_t carry9;
  q = (19 * h9 + (((int32_t)1) << 24)) >> 25;
  q = (h0 + q) >> 26;
  q = (h1 + q) >> 25;
  q = (h2 + q) >> 26;
  q = (h3 + q) >> 25;
  q = (h4 + q) >> 26;
  q = (h5 + q) >> 25;
  q = (h6 + q) >> 26;
  q = (h7 + q) >> 25;
  q = (h8 + q) >> 26;
  q = (h9 + q) >> 25;
  /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
  h0 += 19 * q;
  /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
  carry0 = h0 >> 26;
  h1 += carry0;
  h0 -= carry0 << 26;
  carry1 = h1 >> 25;
  h2 += carry1;
  h1 -= carry1 << 25;
  carry2 = h2 >> 26;
  h3 += carry2;
  h2 -= carry2 << 26;
  carry3 = h3 >> 25;
  h4 += carry3;
  h3 -= carry3 << 25;
  carry4 = h4 >> 26;
  h5 += carry4;
  h4 -= carry4 << 26;
  carry5 = h5 >> 25;
  h6 += carry5;
  h5 -= carry5 << 25;
  carry6 = h6 >> 26;
  h7 += carry6;
  h6 -= carry6 << 26;
  carry7 = h7 >> 25;
  h8 += carry7;
  h7 -= carry7 << 25;
  carry8 = h8 >> 26;
  h9 += carry8;
  h8 -= carry8 << 26;
  carry9 = h9 >> 25;
  h9 -= carry9 << 25;

  /* h10 = carry9 */
  /*
  Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
  Have h0+...+2^230 h9 between 0 and 2^255-1;
  evidently 2^255 h10-2^255 q = 0.
  Goal: Output h0+...+2^230 h9.
  */
  s[0]  = (unsigned char)(h0 >> 0);
  s[1]  = (unsigned char)(h0 >> 8);
  s[2]  = (unsigned char)(h0 >> 16);
  s[3]  = (unsigned char)((h0 >> 24) | (h1 << 2));
  s[4]  = (unsigned char)(h1 >> 6);
  s[5]  = (unsigned char)(h1 >> 14);
  s[6]  = (unsigned char)((h1 >> 22) | (h2 << 3));
  s[7]  = (unsigned char)(h2 >> 5);
  s[8]  = (unsigned char)(h2 >> 13);
  s[9]  = (unsigned char)((h2 >> 21) | (h3 << 5));
  s[10] = (unsigned char)(h3 >> 3);
  s[11] = (unsigned char)(h3 >> 11);
  s[12] = (unsigned char)((h3 >> 19) | (h4 << 6));
  s[13] = (unsigned char)(h4 >> 2);
  s[14] = (unsigned char)(h4 >> 10);
  s[15] = (unsigned char)(h4 >> 18);
  s[16] = (unsigned char)(h5 >> 0);
  s[17] = (unsigned char)(h5 >> 8);
  s[18] = (unsigned char)(h5 >> 16);
  s[19] = (unsigned char)((h5 >> 24) | (h6 << 1));
  s[20] = (unsigned char)(h6 >> 7);
  s[21] = (unsigned char)(h6 >> 15);
  s[22] = (unsigned char)((h6 >> 23) | (h7 << 3));
  s[23] = (unsigned char)(h7 >> 5);
  s[24] = (unsigned char)(h7 >> 13);
  s[25] = (unsigned char)((h7 >> 21) | (h8 << 4));
  s[26] = (unsigned char)(h8 >> 4);
  s[27] = (unsigned char)(h8 >> 12);
  s[28] = (unsigned char)((h8 >> 20) | (h9 << 6));
  s[29] = (unsigned char)(h9 >> 2);
  s[30] = (unsigned char)(h9 >> 10);
  s[31] = (unsigned char)(h9 >> 18);
}
